early 13c., preove "evidence to establish the fact of (something)," from Anglo-French preove, Old French prueve "proof, test, experience" (13c., Modern French preuve), from Late Latin proba "a proof," a back-formation from Latin probare "to prove" (see prove). "The devocalization of v to f ensued upon the loss of final e; cf. the relation of v and f in believe, belief, relieve, relief, behove, behoof, etc. [OED].
Meaning "act of proving" is early 14c. Meaning "act of testing or making trial of anything" is from late 14c., from influence of prove. Meaning "standard of strength of distilled liquor" is from 1705. In photography from 1855. Typographical sense of "trial impression to test type" is from c. 1600. Numismatic sense of "coin struck to test a die" is from 1762; now mostly in reference to coins struck from highly polished dies, mainly for collectors.
Adjectival sense (proof against) is recorded from 1590s, from the noun in expressions such as proof of (mid-15c.), hence extended senses involving "tested power" in compounds such as fireproof (1630s), waterproof (1725), fool-proof (1902), etc. Shakespeare has shame-proof. Expression the proof is in the pudding (1915) is a curious perversion of earlier proof of the pudding is in the eating (1708), with proof in the sense "quality of proving good or turning out well" (17c.); perhaps an advertiser's condensed form of the original.
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